The ABINIT Users Mailing List ( CLOSED )

[Xavier Gonze <gonze@pcpm.ucl.ac.be>]

Dear all,

First, one more paper to look at :

LEVINE ZH, ALLAN DC

LINEAR OPTICAL-RESPONSE IN SILICON AND GERMANIUM INCLUDING SELF-ENERGY EFFECTS 

PHYSICAL REVIEW LETTERS 63 (16): 1719-1722 OCT 16 1989 

It is clear that the denominator has not to be changed in this case, simply because the

wavefunctions are not changed. 

The purpose of the commutator trick is simply to have the action of the operator r .

As mentioned by Fabien, one could use any operator that is periodic and for which

the <v| and |c> are eigenfunctions. So, working first in the LDA wavefunctions

is fine. But then, one should make a unitary transform from the LDA to the scGW wavefunctions,

that span exactly the same space by construction,

and this is not done in the present status of the code. 

Other things that have not been mentioned until now, just to reassure potential users :

- this discussion only concerns self-consistent GW calculations (usual perturbative GW calculations are not concerned)

- moreover, it concerns only one of the q points on which the Brillouin Zone integral has to be done, whose

  weight will get smaller and smaller with the q sampling, and so the converged limit will be OK in any case.

Regards,

Xavier

On 23 Mar 2007, at 18:48, deyulu@yahoo.com wrote:

Fabien:

      Thank you for your explanation, but I don't agree with your argument. 

In doing scissor+G0W0, self-consistent GW on the energies-only, one should use 

H', i.e., H_{KS}+scissor or H_{KS}+Delta sigma, to evaluate quasi-particle energies.

      It applies also to the commutator trick. If we takes the 1st order app.

on H' to assume it is diagonal, one has:

< v | r | c > = < v | [ H' , r ] | c > / (E'_v - E'_c),

where E'_v and E'_c are quasi-particle energies instead of KS energies.

      For a wide range of materials, it has been shown in Fiorentitni and 

Balderesch's paper (PRB, 51:17916, 1995) that the effect of Delta sigma can

be largely attributed to a static screened exchange term, which commutes with r. Then it leads to < v | r | c > = < v | [ H_{KS} , r ] | c > / (E'_v - E'_c).

      In my opinion, this _expression_ is consistent with the formula for G!=0

terms.

     Best

     Deyu***************************************************************************

Deyu Lu (Ph.D)

190 Chemistry Building

University of California, Davis 

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